In chemical processes employing the continuous circulation or transfer of particulate solids, the success or failure of the venture as a whole is often dependent upon the successful operation of the solids transfer system. The large fluidized catalytic cracking (FCC) units used in the petroleum industry and the coal conversion plants to produce synthetic fuels from coal are just two examples of processes where this is true.
Because of the importance of the solids transfer system, its successful design is critical to a process. Unfortunately, the design of such systems can be extremely complex. Gas-solids mixtures (whether pneumatically conveyed or moved in gravity flow in standpipes) can be transported in several different regimes - each with its own inherent quirks and peculiarities. The problem facing the designer of such a system is to couple these various regimes to achieve a smooth, stable transfer of solids over a wide range of operating conditions. This is a difficult task at best but it is made even more difficult because the understanding of many aspects of two-phase gas-solids flow is sadly inadequate. Thus, lacking a sound scientific basis for design, in practice many transport systems are often still designed on the b~sis of operating experience or rules of thumb.
Pneumatic transport of solids can be classified into four different regimes:
horizontal dilute phase flow, vertical dilute phase flow, horizontal dense phase flow, and vertical dense phase flow. The boundary between dilute and dense phase conveying is not clear-cut. The parameter of solids/gas loading (kilograms of solid per kilogram of gas) in the conveying line has often been used to distinguish between dilute and dense phase flow. Solids/gas loadings of 0.01 to 15 kg of solid per kilogram of gas were used to denote dilute phase
341
flow, while dense phase flow was characterized by solids/gas loadings of 15 to over 200 kg of solids per kilogram of gas. However, these are just very rough, rule-of-thumb guidelines, and there can be much overlap. An analysis of each type of conveying is given in the following section.
It is the objective of this chapter to present information which will increase the probability of a successful design of solids transfer systems. In only one chapter there is not space enough for exhaustive theory. Therefore, the emphasis will be placed primarily on practical design.
Line AB is the pressure drop-velocity relationship for gas alone passing through a dilute phase pneumatic conveying line. Curve CDE is for a solids mass flux G1,while curve FG is for a solids mass flux Gz which is greater than G1.At C, the gas velocity is very high and the conveying line is very dilute. As the conveying velocity is decreased from C to D, the gas and solids both rise more slowly. The solids inventory in the lift line rises, thus increasing the static head. However, the frictional resistance portion of the total pressure drop predominates in this region; thus, as the velocity decreases, so does the pressure drop.
In the region D to E, the decreasing velocity results in a rapid increase in solids inventory in the line. The static head of solids now predominates over the frictional resistance and the pressure drop rises. Near E, the bulk density of the mixture becomes too great for the gas velocity to support and the mixture begins to slug, or choke. The superficial gas velocity at E is termed the choking velocity Uch, which is the minimum velocity which can be used to smoothly transport solids in vertical dilute phase conveying lines, and is obviously an important design parameter. The curve FG defines the pressure drop-velocity relationship for a higher mass flux,Gz. Feeding the conveying line at the solids rate Gz will cause the conveying line to choke at a higher gas velocity. Thus, choking can be reached by decreasing the gas velocity at a constant solids flowrate or increasing the solids flowrate at a constant gas velocity.
Although operation near choking will result in the minimum gas require-ment for pneumatic solids transfer, the choking region is a very unstable one.
A small decrease in the gas velocity near choking causes the average pressure drop in the lift line to rise rapidly. This is accompanied by large fluctuations in the pressure drop as the line starts to choke. In large diameter conveying lines the slugging of the solids can also cause excessive vibration which can be structurally damaging if allowed to persist for any length of time.
A good operating point for vertical dilute phase conveying lines is at, or slightly to the right of, D. At this point, the AP/L versus velocity curve is relatively flat, and small perturbations in the system will not cause large changes in the conveying line pressure drop. Lift gas requirements at D are still low and yet far enough away from choking to be 'safe'. Perhaps most importantly, this is the point of minimum lift-line pressure drop.
If centrifugal fans are used to supply the gas for the riser, there is another reason why operation in the region D to E is unsatisfactory. Centrifugal fans are characterized by reduced capacity as outlet pressure is increased. Leung, Wiles, and Nicklin (1971a) have noted that if a slight system perturbation caused an increase in solids flowrate, the pressure drop in the lift line would increase. This would raise the pressure at the outlet of the fan and would . result in a decrease in the output of the fan, producing a lower velocity in the lift line. This would shift the system operating point on the AP/L versus In the design of industrial vertical dilute phase pneumatic conveying systems,
the main consideration is generally that of choosing the correct velocity at which to transport the solids. Too Iowa velocity will result in unacceptable, unstable slugging flow; too high a velocity will result in excessive gas requirements and high pressure drops. The general relationship between velocity and pressure drop per unit length, AP/ L, in a dilute phase vertical riser is shown schematically in Fig. 12.1.
FRICTIONAL RESISTANCE PREDOMINATES
SLPERFICIAL VELOCITY, U
Figure 12.1 Phase diagram for dilute phase vertical pneumatic conveying.
velocity curve towards E, producing a further increase in the system pressure drop. This cycle would continue until choking conditions were reached, resulting in unstable flow in the pipe. This destructive cycle does not occur if the fan operates at velocities to the right of D.
Zenz and Othmer (1960) are generally considered to be the first to describe choking. They considered it to be the degeneration of dilute gas-solids flow into dense, slugging flow. Matsen (1981) and Yang (1982) have recently suggested that choking occurs because of the formation of clusters or particle aggregates. Indeed, Grace and Tuot (1979), through instability analysis, showed that a uniform gas-solid suspension is unstable and that there is a tendency for clusters to form (see Chapter 7).
However, not every gas-solids mixture will choke. It is possible for solids to undergo a transition from a dilute phase directly to a denser non-choking, fluidized bed type of transport. Yousfi and Gau (1974) were the first to observe such a transition, and developed a criterion to precit when choking ,would occur; i.e.:
v2
g~ >140 for choking to occur (12.1)
Yang (1976a) extended this concept further and developed the following criterion for choking:
appears to be a pneumatic conveying line operating in the relatively dense phase region near choking. This has been proposed by both Yang (1982) and Matsen (1981). Indeed, Gajdos and BierI (1978), using probe measurements and X-ray exposures, reported that fast fluidization was phenomenologically no different than classical dilute phase conveying. Both regimes were found to consist of high velocity dilute core, surround by a low velocity dense annulus.
This annular core flow in a riser has also been reported by Batholomew and Casagrande (1957), Van Zoonen (1961), and Saxton and Worley (1970).
12.2.1 Particle Velocity
The particle velocity in vertical dilute phase conveying lines is an important parameter because it determines the residence time of the solids in the line.
The solids velocity in the conveying line differs from the gas velocity in the line by the slip velocity:
Fr= -<
vf
0.35 gD > 0.35v,
= IV
g - v'lipl
(12.4)The slip velocity is often approximated by the terminal velocity of the particles, and if this assumption is made, Eq. (12.4) becomes:
v, = IV
g -vtl
(12.5)Measurements by Hinkle (1953) using high speed photography and coarse particles, showed that this relationship applied within ±20 per cent. Capes and Nakamura (1973) trapped a wide variety of solids in a 7.6 cm diameter riser to determine particle velocities and concluded: (a) that slip velocity was often greater than the terminal velocity and (b) that the deviation between
V,lip and Vt was greater for particles with high terminal velocities. This was attributed to particle-to-wall friction and particle recirculation in the lift line.
However, their data also indicate that for particles with terminal velocities below 7.6 mis, Eq. (12.5) can be used as a reasonable approximation.
Matsen (1981) has proposed that the slip velocity is basically only a function of the voidage of the dilute, flowing suspension. He argues that as the voidage decreases (due to increased solids loading, for example) the slip velocity increases. He attributes this to cluster formation, but a solids annular flow model would also explain this voidage-slip velocity relationship.
no choking choking occurs
This criterion (which is based on the maximum stable bubble size theory of Davidson and Harrison, 1963) predicts that light and small materials are less likely to choke, and takes into account the diameter of the line being employed.
A third criterion for choking was proposed by Smith (1978):
Vt f!"'-I n (1 - e)
05 >0.41 (gD) .
Leung (1980) considered these three choking criteria and concluded that Yang's criterion was most useful since it contained the important parameter of pipe size and was most consistent with the experimental data.
The concept that not all materials will choke is also supported by the work of Canning and Thompson (1980). They found that large diameter particles invariably formed slugs in vertical (and horizontal) pneumatic conveying, while finer solids did not tend to slug.
The 'fast fluidized bed' (see Chapter 7) researched extensively by workers at the City College of New York (Yerushalmi, Turner, and Squires, 1976)
12.2.2 Choking Velocity Correlations
In spite of the extensive literature on all aspects of pneumatic conveying; the most reliable way to determine design parameters for a particular pneumatic conveying system is still by experiment. This generally requires the construction and operation of a test rig, but this is not always possible because
SOLIDS TRANSFER IN FLUIDIZED SYSTEMS 347
Figure 12.2 The effect of gas density on choking velocity (Knowlton and Bachovchin, 1976).
of insufficient time and/or funds. There are, however, numerous correlations for predicting conveying design parameters - so many, in fact, that a designer could easily feel like the proverbial mosquito in a nudist colony -he just would not know where to begin! Comparisons of many of these correlations have been published, and although somewhat limited, the comparisons provide a reference point for discussion.
The choking velocity defines the lower limit of the gas velocity for a dilute phase vertical pneumatic conveying system. A comparative study of several choking velocity correlations was carried out by the Institute of Gas Technology for the US Department of Energy (Institute of Gas Technology, 1978). This report has an extensive review of the available choking velocity correlations. The correlations of Zenz (1964), Rose and Duckworth (1969), Leung, Wiles, and Nicklin (1971a), Yousfi and Gau (1974), Knowlton and Bachovchin (1976), Yang (1975), and Punwani, Modi and Tarman (1976) were evaluated using both low pressure and high pressure data. The correlation of Punwani, Modi, and Tarman (1976) was recommended for use in predicting choking velocities. This correlation is basically the Yang (1975) correlation modified to take into account the considerable effect of gas density on choking velocity shown by Knowlton and Bachovchin (1976). The substantial dependence of Uch on gas density is illustrated in Fig. 12.2. The Punwani correlation is shown below:
2gD (E-4.7 - 1)
A worked example of how to calculate the choking velocity using the Punwani correlation is shown below.
To calculate the actual gas velocity at choking, Eqs (12.6) and (12.7) must be solved simultaneously for Ech and Vch' This correlation predicted the -data tested within 25 per cent.
Yang (1982) has recently modified his earlier choking velocity correlation to include the effect of gas density. The modified Yang choking velocity correlation is also shown below:
. 2gD (E~4.7 - 1) _ 5
(.!!1..).2.2
Example 12.1: Choking velocity calculation - Punwani correlation Calculate the choking velocity for coal particles with an average particle size of 300 ~m being conveyed at a rate of 1,816 kg/h using nitrogen in a 75 mm diameter pipe at a system temperature of 20°C and a system pressure of 17 bar gauge.
Solving the Punwani correlation for the choking velocity consists of solving Eqs. (12.6) and (12.7) simultaneously for Vch and Ech'
In order to calculate the choking velocity a value must be obtained for the terminal velocity VI> the method outlined in Chapter 6, Section 6.3, may be used; alternatively, since the flow regime is transitional, Eq. (12.11) is appropriate. Assume that the particle size given in the example is the volume diameter dv.
0.153go.71d~.14 (pp _ pg)O.71
VI
=
p~.29 /LO.43For the conditions given:
and presented in the Coal Conversion Systems Technical Data Book (Institute of Gas Technology, 1978). Several of these correlations (Hinkle, 1953; Currin and Gorin, 1968; Konno and Saito, 1969; Rose and Duckworth, 1969;
Richards and Wiersma, 1973; Knowlton and Bachovchin, 1976; Leung, 1976;
and Yang, 1976) were compared in the Data Book using the low pressure data of Curran and Gorin (1968) and the high pressure data of Knowlton and Bachovchin (1976). The correlation of Yang was found to predict the low pressure data better than the other correlations. However, overall, the modified Konno and Saito correlation was found to predict the data somewhat better than the Yang correlation and, although much less sophisticated than the Yang correlation, is much simpler to use. The modified Konno and Saito correlation is presented below:
_ U2Pg G 2fgPgU2L 0.057Upg8Lg
6.PT - 2
+
sVs+
D+
v'(gD)(1) (2) (3) (4) (6)
(12.12)
Gs
Vs
= - =
0.095 m/sPp
Equations (12.6) and (12.7) then become:
2 x 9.81 x 0.076 (E.;4.7 - 1)
(Vch _ 0.5)2
=
8.72 X 10-3 x (21.6)°·77(Vch - 0.5) (1 - Ech)
=
0.095 Combining the equations we have:(E~h4.7- 1) (1 - ECh)2
=
5.69 X 10-4Using the trial and error method:
Ech
=
0.95280.095 1-Ech
=
2.51 mlsUch
=
Vch Ech=
2.51 x 0.9528=
2.39 m/sGs Vs
=
vg - VI and 8=--UPg
and where the numbered terms have the following significance:
(1) pressure drop due to gas acceleration, (2) presure drop due to particle acceleration, (3) pressure drop due to gas-to-pipe friction, (4) pressure drop related to solid-to-pipe friction, (5) pressure drop due to the static head of the solids, (6) pressure drop due to the static head of the gas.
If the gas and the solids are already accelerated in the lift line, then the first two terms should be omitted from the calculation of the pressure drop.
A worked example of how to calculate the pressure drop in vertical dilute phase pneumatic conveying using the Konno and Saito correlation is given below.
12.2.3 Vertical Dilute Phase Pressure Drop Corre/Qtion
Many correlations are also available for use in determining the pressure drop in vertical pneumatic conveying lines. Twenty such correlations were found
Example 12.2: Pressure drop in vertical dilute phase conveying-Konno and Saito method
Determine the pressure drop in a dilute·phase pneumatic conveying line in which coal of an average particle size of 300 /Lm is being conveyed at a velocity of 12mls with nitrogen in a 75 mm diameter conveying line at a rate of 1,861 kg/h. The temperature of the line is 21°C and is at a pressure of 17 bar guage. The line is 15 m long.
Solution
Assume the gas is already accelerated when the particles enter the line. Since the gas is already accelerated then, from Eg. (12.12):
2fgPgU2L 0.057UpgfJLg GsLg
APT
=
Gsvs + D + V(gD) + ~ + PgLg (12.13)=(12 - 0.5) m/s
=11.5m/s
Gs 114
9
= -- = ----
0.44 kg solid/kg gasUPg 12 x 21.6 I
2fg x 21.6X (12)2 x 15 0.057 x 12 x 21.6 x 0.44 x 15 x 9.81 AP
=
114 x11.5+---+---··-·-·---T 0.075 V(9.81 x 0.075)
114 x 15 x 9.81
+
11.5 + 21.6 x 15 x 9.81To calculate the Reynolds number to determine the friction factor we have:
DUpg 0.075 x 12 x 21.6 6
Re
=
-fJ--=
1.84X 10-5=
1.06 x 10and
fg
=0.004 Therefore:6..PT
=
1,311 + 4,976 + 1,115 + 1,459+
3,178=
12,039 N/m2 Since 10 ,000N/m2=
1.45 Ib/in2:APT
=
1.74lb/in2As in vertical dilute phase pneumatic conveying, the problem confronting the designer of a horizontal dilute phase transfer line is selecting a suitable gas velocity. The general relationship between superficial velocity and API L for a horizontal dilute phase transfer line is sho~n in Fig. 12.3. In many ways this relationship is similar to that for a vertical dilute phase conveying line. Line AB represents the curve obtained for gas alone travelling through the pipe,
I
~z
W..J f-....•
Z::l
~ ,6p WQ. L
Q.
o~ a w~
::len enw
~Q.
@
".a..:...
••".::.:.
curve CDEF for a mass flux G1, and curve GH for a mass flux G2 greater than G1•At C, the gas velocity in the horizontal line is sufficiently high to carry solids at a rate G1through the pipe in a very dilute suspension. If the gas velocity is reduced while continuing to feed at the constant mass flux G1,the frictional resistance, and thus the pressure drop in the line, will decrease. The solids will move more slowly and their concentration in the pipe will increase.
AtD,the gas velocity is insufficient to keep the solids in suspension, and they begin to settle to the bottom of the pipe. The gas velocity at D is termed the saltation velocity, Usa1t>and is a strong function of solids loading.
If the gas velocity is reduced further to E, the pressure drop will rise rapidly as the solids continue to deposit on the bottom of the pipe constricting the space available for gas flow. As the gas velocity is reduced between E and F, the depth of the particle layer and the pressure gradient both increase. In this regime, some particles may move slowly in dense phase flow along the bottom of the pipe, while, simultaneously, others travel in suspension in the gas in the upper part of the pipe.
The saltation velocity sets a lower limit on velocity for any horizontal dilute phase pneumatic transfer ~s-tem. It is desirable, however, to oper-ate at as low a velocity and pressure drop as possible and still remain far enough from saltation to be 'safe' if a system upset should occur. Therefore,
the saltation velocity needs to be determined to set a lower bound on this operating point.
12.3.1 Saltation Velocity Correlation
There have been many efforts to correlate the saltation velocity. Two comparisons of many of the published saltation velocity correlations have been made (Jones and Leung, 1978; and Arastoopour et al., 1979). The Jones and Leung comparison was made using eight different correlations (Thomas, 1962; Doig and Roper, 1963; Zenz, 1964; Rose and Duckworth, 1969; Rizk, 1973; Matsumoto etal., 1974a, 1975b; Mewing, 1976). The comparisons were made using air-solids data only, and at low pressure. Jones and Leung recommended that the Thomas correlation be used for design.
The Zenz correlation predicts that as particle size is decreased, the saltation velocity at first decreases, then passes through a minimum, and then increases again. This latter effect is explained as being due to small particles becoming 'trapped' in the laminar sublayer and needing a higher velocity to dislodge the particle. However, for small particles (less than about 80JLm in size), the Zenz correlation at times predicts unbelievably high values of the saltation velocity. It is best applied to particles larger than this size.
A worked example of how to calculate the saltation velocity using the Zenz correlation is shown below.
CONVEYING MEDIUM, AIR SPHERICAL PARTICLES ---- ANGULAR PARTICLES
Figure 12.4 Single-particle saltation velocities as a function of particle size in a 63.5 mm diameter lucite tube (Zenz, 1964).
w
= /
1
113(the units of ware in metres per second)
Example 12.3: Calculation of saltation velocity-method of Zem;
Calculate the saltation velocity of -10+ 100 US mesh sand being conveyed at a rate of 1,362 kg/h through a 150 mm diameter tube with nitrogen at 21°C
Calculate the saltation velocity of -10+ 100 US mesh sand being conveyed at a rate of 1,362 kg/h through a 150 mm diameter tube with nitrogen at 21°C